Chap 1 (motion) archived stories part F

Saturday, February 07, 2009

For Chapter 1, here is part F of the new stories and also the updates to the items in the book, including many video links and journal citations. If you want all the video links (hundreds) and journal citations (thousands) for this chapter, go to

1.210 Criss Angel magic --- floating between two buildingsJearl Walkerwww.flyingcircusofphysics.comOct 2008 Can you float between buildings? Well, here is a link to watch magician Criss Angel float between two buildings, but before you continue, let me warn that if you don’t want the magic trick to be spoiled, don’t read past the link.

Yes, of course, Criss Angel can no more float between buildings than you can, but the challenge here is to explain how he performs the illusion. There is a physics clue in the early part of the video and another in the last part. Did you spot them?

First, let’s dismiss the idea of innocent onlookers. The young men on the rooftop are in on the trick but they give us the impression that nothing unusual is happening off camera. However, what they can see is a tall industrial crane with its upper end above Angel. Thin wires run from that upper end down to a harness that is hidden beneath Angel's clothing. The wires are too thin for us to see in the video’s resolution, which I assume was originally shot on videotape, certainly not as a high-definition digital recording. The wires are also hidden from our view because of clever shooting by the camera crew --- they are shooting toward a bright background sky.

When Angel talks to the young men on the roof, the wires are slack enough to allow him to walk across the roof. When he prepares himself to levitate, the top of the crane moves upward and the wires are pulled taut, which lifts him from the roof. The physics clue lies in that liftoff.

In order to be stable, Angel must always have his center of mass (which is behind the navel) vertically aligned with his support. When he is standing, the support is his feet and his center of mass is positioned over his feet. But when he is lifted off the roof, the support is on the wires attached to the front of the harness. Initially, the center of mass is behind that support but then the lower part of his body swings forward to bring the center of mass under the support point. He tries to hide this motion by leaning the top half of his body forward, but he cannot completely stop the forward rotation of his legs.

The crane gradually rotates so as to carry Angel to the second roof, where he lands. In the landing, notice that he immediately leans forward. He lands with his feet ahead of the center of mass, and thus he must lean forward to get the center of mass back over the feet or he would have toppled backwards when the support wires went slack.

Although the magic here relies primarily on our inability to see what is off camera or what is too thin to be picked up on videotape, especially with a bright background sky. the trick is still impressive.

1.211 Motorcycle Ball of DeathJearl Walkerwww.flyingcircusofphysics.comNov 2008 In this very dangerous circus show, a motorcyclist rides a motorbike inside a sphere consisting of a rigid metal mesh. We can see the rider through the mesh as he rides around the interior, circling below the “equator” of the sphere or along a tilted “orbit” that takes him high and low. Here is a link that shows first a single performer and then two performers.

My favorite, however, shows a sideshow performance on a “wall of death” (rather than a sphere). The rider not only takes his large motorcycle up on a circular wall, but then rides while his hands are off the handlebars, his legs are up off the motorcycle, and he is sitting sideways. Never mind that all the while he is roaring around the interior of the curved wall, seemingly in defiance of gravity.

You can find many more links below, at the end of this item. In all the stunts, the question is obvious: How does a rider avoid merely falling over? To answer, let’s first consider a less dangerous but fairly common amusement park ride --- the Rotor. Here is a link to a television show in which I ride in a Rotor. Choose “video” below my picture on the left. Then scroll down to the menu of videos and choose Episode 2. The rotor comes up about 3 minutes into the video.

To ride the Rotor, I enter a large vertical cylinder and stand against the interior wall. The cylinder then begins to rotate around the central vertical axis. As the speed increases, I begin to feel an outward force (radially outward), especially on my torso, as if something is pressing against my chest. When the speed is fast enough, the floor in the cylinder drops away, leaving me suspended on the wall. The apparent force on me pins me there, much like a butterfly specimen is pinned to a wall in a butterfly collection.

The gravitational force is pulling me down, so why don’t I slide down the wall to reach the floor? That downward force is countered by an upward frictional force between my clothes and the wall. However, if the cylinder turned only slowly, the frictional force could not be that large and I would slide down. The ride operator knows to wait until I am turning very fast before the floor is dropped away from me. I move in a circular path because the wall pushes on me. Oh, I don’t move toward the center of the cylinder but the wall still pushes inward on me to make me follow the circular path. The faster I rotate, the greater that inward push must be. And the greater that push is, the greater the frictional force can be without allowing me to slide down the wall.

Now, that is the way a person watching me would explain the forces but, moving around in the circle, I would disagree. I have a very clear sensation of being pushed into the wall by an outward force --- I have that sensation in spite of the fact there is nothing actually pushing me in that direction. This illusionary force is, nevertheless, very convincing. The true force on me is a centripetal force (toward the center) from the wall, not a centrifugal force (outward from the center) from some invisible person pressing on my chest.

These same forces are involved in a ball-of-death stunt. Let’s consider the motorbike and rider as being a single object. When the path is along the equator, the wheels press against a vertical wall because that part of the curved interior of the ball is vertical. So, the situation should be identical to me in the Rotor. However, the motorbike and rider extend farther from the wall than I did and are in danger of rotating downward around the point of contact between the wheels and the wall. To avoid that rotation, the rider tilts the bike somewhat upward so that he and the bike are somewhat above the horizontal circle taken along the equator. Because the rider is moving in a circle, he senses a centrifugal force (just as I did in the Rotor) that tends to rotate him upward around the contact point. To him, this tendency of upward rotation balances the tendency of downward rotation, and that is why he is stable.

Of course, the gravitational force tends to pull him and the motorbike downward, but an upward frictional force on the wheels from the wall matches that downward pull (just as the frictional force on my clothes matches the downward pull).

The story is about the same when the rider takes a horizontal path below the equator, except that now, with the wall slanted instead of vertical, the force from the wall is partially upward and helps support the rider. For a tilted orbit, the arguments are about the same except that the gravitational force need not be matched. For example, when the rider goes through the highest point of the ball, he and the motorbike are actually falling. However, they don’t merely fall straight down because they are still traveling in a forward direction along the path. So, in a sense, they fall down along that path, until they reach the lower section.

In 1998, Kirk T. McDonald of Princeton University analyzed the circular orbits inside the Ball of Death, showing the stability of horizontal orbits around the equator and below the equator and vertical orbits from pole to pole. Surprisingly, he also found that a horizontal orbit above the equator might be stable. However, I cannot find a video example where a rider attempted such a dangerous orbit. There would a huge leap of faith in going from a theoretical calculation to actually trying to circle in the top half of the ball.

In terms of the mantra for the Flying Circus of Physics book: Physics is everywhere, especially in death-defying stunts at a circus.

http://www.youtube.com/watch?v=VzKBvtsICwQ Initially, three just below the equator and two well below the equator. Hand-held camera in the audience. Then one motorcycle takes a high “polar” path, passing through the others twice per orbit.

http://www.youtube.com/watch?v=rUVXNeHa5EA&feature=related motorcycle on an actual wall rather than inside a sphere, rides with hands off the handle bars and then while standing on the bike and then while standing with the hands off the handlebars and then while sitting sideways, first one way and then the other

1.212 Bursting balloonJearl Walkerwww.flyingcircusofphysics.comNov 2008 Thanks to high-speed photography (and also thanks to video outlets like YouTube), we can now see details of the bursting of a balloon.

Here are several links to high-speed videos of water balloons being burst.

Notice two features: 1. The balloon contracts faster than the water can respond to the gravitational force, so the water is still in place when the polymer sheath that had held it has vanished. Thus, we can conclude that the forces involve in the polymer contraction are much greater than the gravitational force that causes the water to slump.

2. In one video we see that the balloon wall does not merely contract but becomes wavy, resembling a water wave. Any such wave appearance makes the pulse of a physicist race because it signals that an instability is involved. As the torn edge of the balloon is pulled around to the “back” of the balloon, forces cause the wall to bulge inward and outward in a wavy pattern. As this wavy balloon wall slides over the water, the water surface is disturbed, sending spray into the air.

Popping balloons is not only fun but it is interesting to physicists and materials scientists because the burst is an example of a quickly traveling crack in a polymer under stress. Such cracking is not well understood but is important in the fatigue and failure of polymers in many common applications.

Here is one feature that came as a surprise: The crack is often not straight but oscillates sideways as it travels through the polymer. The photograph here shows curvy edges along pieces of a (Power Rangers) balloon that I inflated and then popped with a knife point. I don’t understand what features determine where the edges are straight and where they have sine-wave appearance. You might experiment with stretching rubber sheets between two supports (such as a vise) and between four supports (such as on a picture frame). Does the extent of stretching in one direction or in both directions determine what type of crack occurs?

The following link takes you to a very slow-motion video of a water-filled balloon being popped.

If you repeatedly hit the pause and continue button so as to step through the popping footage, you can see a curvy edge on the retreating balloon wall as it pulls along the enclosed water. The prick of the tack used to pierce the balloon produces a vertical crack in the balloon wall. As you step through the footage, note that the initial crack leaves an indentation in the water that is still evident even as the balloon wall is about to move rightward out of the shot.

1.213 Pub trick --- removing the cork from a wine bottleJearl Walkerwww.flyingcircusofphysics.comJan 2009 First, after a wine bottle is emptied and the cork is pushed back through the neck so that it is loose within the body of the bottle, you are hit with two challenges. How can you remove the cork without breaking the bottle? And how does the removal technique work? (Remember, anyone can show off but the power of physics is the ability to explain.) Here are two similar videos showing how to remove the cork but neither explains the trick.

Notice that after the plastic bag is inserted into the bottle, it is not just pulled back out because then it would simply slide past the cork. Instead, it is partially inflated and then (here is the real secret) the free end of the bag is twisted so as to trap the air in the inflated part. The bag is not airtight, but as it is pulled out of the bottle, the air in the inflated part is still largely trapped and that part presses against the glass wall, acting like a plunger as it pushes the cork into the neck.

Physics is everywhere and maybe especially in pubs.

1.214 Puzzle --- bridge collapse under weight of a houseJearl Walkerwww.flyingcircusofphysics.comJan 2009 These photos have been on the web for several years but without any explanation of what exactly went wrong as the house was being moved across the short bridge, from one side of a stream to the other.

Obviously the weight broke the bridge but isn’t it curious that the collapse did not occur until the midpoint of the house was over the bridge? Why didn’t the bridge collapse as the truck first began to move over the bridge? Is there any evidence to help us explain how the collapse occurred or, more to the point, what error was made in planning the move?

Notice that the house is supported by a long steel beam on each side and that a flatbed with wheels is attached to the underside of each beam. On each side we can see two sets of four wheels (with two wheels on each side of the beam), giving a total of 8 wheels on each side of the house. However, notice that another two more sets of four wheels lie on the collapsed second bridge section, below the flatbed. Thus, there were originally 12 wheels on each side of the house, at the midpoint of each beam.

Next, notice that the beams rest directly on the road on both sides of the bridge, suggesting that there are no wheel supports on the front or rear end of the house.

Thus, the house weight was supported in only two regions: somewhat by the hitching point where the beams were attached to the truck but primarily by the flatbed at the midpoint.

When the truck moved over the bridge, the bridge had to support the truck’s weight and a fraction of the house’s weight. After the truck passed over the bridge and before the flatbed reached the bridge, the bridge did not support any weight. Then, as the flatbed began to move over the bridge, the bridge had to support nearly the full weight of the house. The first section of bridge was sturdy enough to do that, but when the flatbed reached where the second and third sections of bridge butted together, the sections buckled and then collapsed. As the sections buckled, the mounting of one set of wheels on each side was bent so severely that the wheels broke off, landing on the collapsed second section of the bridge.

Obviously, distributing the load over more flatbeds of wheels (one at the front, one at the midpoint, and one at the rear) would have been a better plan in moving the house over the bridge. Of course, obvious solutions are usually obvious only after an accident.

1.215 Pedestrian throw, moose throw, camel throwJearl Walkerwww.flyingcircusofphysics.comJan 2009 One unfortunate example of physics in the everyday world involves the collision between a moving road vehicle and either a pedestrian or a large animal such as a moose or camel. The forensic reconstruction of such an accident, in which not only the victim but also the driver may be killed, is often required in police investigations. The physics of pedestrian throw can be put into four general categories. In each, the collision of the vehicle causes the pedestrian to move in the direction of vehicle's travel, because momentum is transferred from the vehicle to the pedestrian. However, in some of the accidents, the pedestrian undergoes a second collision with the hood (bonnet)and is thrown up into the air. Depending on whether the vehicle is being slowed, the person might then land in front of the vehicle, on top of it, or even behind it.

1. In a wrap, the initial impact of the car front, either the bumper or grill, shoves the legs from under the torso by either sweeping out the legs, buckling the legs at the knees, or breaking the legs or knees. The pedestrian tends to rotate around his center of mass until the hood hits him. He then wraps around the front of the car, with his chest landing on the top of the hood and then, slightly later, the head striking the hood.

The victim may remain on the hood like this until the car stops but if the car is being rapidly slowed by the (horrified) driver, the hood slides under the body, leaving the body with the forward motion it obtained from the car. The victim then lands in front of the car, with the feet landing farther from the car than the head. (The body’s orientation is one of the forensic clues to an investigator.)

The following video shows a wrap collision and also the next type of collision (don’t worry, the victims in the video walk away from the accidents).

2. In a fender vault, the collision occurs at a front corner of the car and the victim is wrapped over the hood but immediately comes off to one side of the car’s path. Again, the victim lands with the feet farther from the car than the head.

3. In forward projection, the pedestrian is hit by a vehicle with a high front, such as on a bus, and there is no chance for a wrap. Instead, the victim is hurled forward by the impact and lands with the head farther from the vehicle than the feet. (Note this orientation is opposite that in the first two types of pedestrian throw.)

4. In a roof vault, the collision is similar to a wrap in that the leg support is eliminated and the curved front of the car hits the victim but that impact is too severe for the victim to lie on the hood. Instead, the victim is thrown up into the air with a lot of rotation around the center of mass. While the victim is airborne, the car continues to move forward, and the victim probably lands behind the car. The following videos show roof vaulting. Caution: although these videos do not show close-up views of the victims, the motion is still graphic. The first victim (who is hit at the left side of the intersection and who lands in the middle of the intersection) lived through the accident. However, the collision in the second video was probably fatal; I cringe every time I watch it.

5. In a somersault, the collision is similar to roof vaulting but the vehicle is rapidly slowing. The victim is hurled upward and forward but lands in front of the stopped car.

The challenge of the physics research in these types of collisions is to use the forensic evidence (including the orientation of the victim, the projection distance, the damage to the victim’s legs, and the damage to the vehicle) to determine the vehicle’s speed and the pedestrian’s location at the instant of the collision. Obviously, a forensic investigator wants to determine if the speed was in excess of the speed limit and whether the pedestrian was legally crossing the road.

The horizontal distance in a pedestrian throw is related to the vehicle speed but the calculation is tricky because many variables are involved. However, the damage to the legs is more obvious: the low bumper of a sedan damages the lower leg (tibia) and the knees whereas the higher bumper of a SUV or pickup truck damages the upper leg (femur).

When a vehicle hits a large animal such as deer, moose, elk, or cow, the animal usually warps onto the hood. If the animal is mature, its mass is much greater than that of a pedestrian and may be almost as much as the vehicle’s mass. Thus the damage to the hood is more extensive. More serious, however, is that the hood may slide under the animal so that the windshield and then the driver collide with the animal. Such collisions are usually fatal to both the animal and the driver. (Caution: In some of the following vital links, the animals, mostly deer, are killed by the collisions.)

In Anchorage, Alaska, collisions of a vehicle with a moose are so common that the police refer to them with the abbreviation MVC. Similarly, in Saudi Arabia, police refer to collisions with camels as CVC. Here is a video showing the aftermath of small car hitting a camel. The car is destroyed and the camel is seemingly dead. But then suddenly the camel stands up and walks on down the road, probably in a very bad mood.

1.215 Moose-car collisionsJearl Walkerwww.flyingcircusofphysics.comMay 2014 In Anchorage, Alaska, collisions of a vehicle with a moose are so common that they are referred to with the abbreviation MVC. A similar danger occurs in Saudi Arabia because of camel-vehicle collisions (CVC). In either case, the center of mass of the animal is high from the ground. So, when a common car hits the animal, its legs are knocked out from under it and the body is rotated around a horizontal axis as the front of the car travels under it. The result is that the animal crashes into the windshield or down on to the front of the car’s roof. Here is a video showing researchers at Volvo simulating MVC, to determine the damage their cars would suffer in such collisions:

The physics of collisions is part of every standard physics textbook but usually the collisions are between “blocks” or “boxes,” rarely anything real or alive. However, here is a realistic example from my textbook, Halliday Resnick Walker Fundamentals of Physics:

Suppose a 1000 kg car slides into a stationary 500 kg moose on a very slippery road, with the moose being thrown through the windshield. Because the road is very slippery and the collision is brief, we can conserve momentum (the product of mass and speed) in the collision. Before the collision, the only momentum is that of the car. After the collision, the car and moose travel together (the collision is completely inelastic, meaning that the colliding objects stick together). Solving the equation for the conservation of momentum, we find that the speed of the car and moose right after the collision is 2/3 of the car’s original speed --- the speed is less because the amount of moving mass has increased. Perhaps more important, about 1/3 of the car’s original kinetic energy is lost to damaging the car and moose. If you are in front seat of the vehicle, you can be killed. The learning objective here: If you live in moose country (or camel country), slow down or you might get antlers up the nose.

x1.216 “Hang on a minute, lads. I’ve got a great idea.”Jearl Walkerwww.flyingcircusofphysics.comFeb 2009 Arguably, the greatest cliffhanger in movie history occurred in the original version of The Italian Job, when Charlie Croker (played by Michael Caine) is stretched out on the floor of a bus while the bus straddles a narrow wall along a road in the Alps.

Croker and his gang have just stolen a heavy load of gold bars and are escaping in the bus when the bus slides out of control on a curve and ends up barely balanced on the wall, with half of it hanging over the road and half hanging over a steep mountainside, over a very long fall.

Initially, everyone on board the bus moves to the driver’s end of the bus, to counterbalance the heavy load of gold near the rear of the empty floor of the bus. When Croker tries to crawl to the gold, he makes the situation worse because he shifts the center of mass of the bus-gold-people system toward the rear of the bus. As a result the bus tilts downward on that end and the gold slides to the rear door, increasing the tilt.

If Croker moves any closer to the gold, the resulting shift in the center of mass will tilt the bus completely over the wall and into the long fall down the mountainside. Worse, the bus will tilt over into the fall even if one of the gang members leaves the driver’s end of the bus. So, the situation seems hopeless.

Here is a link to the end of the movie. (At least this link will work until Paramount Pictures, who owns the copyrights to the movie, has it removed from YouTube. Then you’ll have to rent the movie.)

We last see Crocker splayed on the bus floor, hardly daring to move as he calls out, “Hang on a minute, lads. I’ve got a great idea.” But then the movie ends, with no clue about his great idea on retrieving the gold or even getting off the bus alive.

Long after he made the movie, Michael Caine explained an alternative ending to the movie: He was to crawl back to the driver’s seat and start up the engine as everyone else stayed in place. The fuel tank under the bus extended out toward the rear of the bus and thus was out past the supporting wall. So, as the fuel was consumed by the engine, the weight on the rear part of the bus would decrease, shifting the center of mass of the system toward the road. As it passed the wall, the bus would have tilted down onto the road, allowing the gang members to escape. Of course, using up a full tank of fuel would have taken quite a long time.

To mark the 40th anniversary of the movie, The Royal Society of Chemistry in the UK ran a contest: How can Croker and his band of thieves escape from the bus, with or without the gold, in a short amount of time? Down below here, I’ve put links to several of the news stories that appeared when the contest winner was announced last month.

Solutions ranged from silly to serious and from practical to highly impractical. One involved melting the road in order to glue down the tires (but someone had to escape the bus in order to do that and, besides, the tires were not touching the road). Another involved the quantum mechanical effect known as the Casimir effect, in which two nearby surfaces will be pushed together by the virtual particles that continuously appear and disappear, even in a vacuum. Uhm, I don’t think the Casimir effect works in the everyday world, not even on a movie set.

The winner of the contest had this plan:

1. The windows above the front tires would be smashed so that someone could be lowered down the side of the bus to deflate the tires, so that if that end of the bus descends, it won’t merely bounce off the road.

2. To offset the loss of weight due to the smashed windows on the driver’s end of the bus, Croker would first smash the windows out near where we see him crawl.

3. He would then open a panel in the floor of the bus (yes, there is one) where he could reach the drain control on the fuel tank. The fuel would pour out, reducing the weight on the suspended back end of the bus and causing the bus to tilt back onto the road.

4. One of the gang members could then safely leave the bus in order to load rocks into the driver’s end of the bus. As the rock load increased, Crocker could slide to the gold and begin to retrieve it. Moving the gold toward the driver’s end of the bus would further stabilize the bus, and the rest of the gang could then escape.

That sounds like a pretty good plan but I have a nagging question.

When we last see him, why didn’t Croker crawl back to the front of the bus and break the front window so that many of the gang members could crawl through it and then hang from it? That action would have shifted the center of mass toward the road enough for one of the gang to leave the bus so that he could return with rocks. Eventually, with enough rocks onboard, Croker would have been able to slide out to the gold and begin shifting it back to the front end.

All right, all right. I know. I’m spoiling the magic of the cliffhanger. I’ll stop. But have you got any good ideas?

1.217 Pub trick --- balancing a hammer and a lorry Jearl Walkerwww.flyingcircusofphysics.comFeb 2009 A common pub (or even classroom) challenge is to balance various objects on an edge, such as that of a table, bottle, or drinking glass. Here are four examples.

1. A hammer and a plastic ruler are balanced on the edge of a table in a seemingly impossible way. (No, they are not glued in place.)

2. A fork and a spoon are balanced on one end of a matchstick while the matchstick straddles the edge of glass. And then the match stick is burnt so that it only touches the glass on one end rather than straddling it, and yet the fork and spoon still do not fall.

All right, I realize the last one is not a pub trick, but the physics is similar to that of the other tricks here --- the assembly is balanced if its center of mass lies on a vertical line through the support. When something is balanced on a point or an edge, the gravitational force tends to make it unstable, causing it to rotate around the point or edge and then fall. For example, if you are on tightrope (circus high wire), the gravitational force acting on you tends to rotate you around your contact with the rope, causing you to fall. However, if you keep your center of mass (the center point of your mass distribution) on a vertical line through the rope, the gravitational force cannot rotate you. We say that the torque due to that force is zero for such an alignment and that you are in an unstable equilibrium, which means that even a slight disturbance can upset the stability.

The same story applies to, say, the hammer and ruler that are balanced. Yes, they extend outward from the table’s edge, but their combined center of mass is on a vertical line through that edge.

The story might also explain the dangling lorry. The center of mass of the entire lorry (the dangling rear section and the front tractor) might be on a vertical line through the supporting “edge” of the rear wheels of the tractor. However, if the tractor is very heavy and the rear section is very light, the center of mass might be farther from the supporting edge. In that case, the situation might be difficult to fix but the tractor is not in danger of being rotated around the supporting edge, to fall into the water.1.218 Landing an airplane on waterJearl Walkerwww.flyingcircusofphysics.comFeb 2009 When Captain Chesley Sullenberger III landed Flight 1549 on the Hudson River, various news sources repeatedly emphasized just how dangerous a water landing is. Yes, crash landing is obviously dangerous but what exactly is especially dangerous about a water landing? You can see clues in this video of a hijacked airplane that was forced to land on water.

As you can tell from these two videos, the airplane wings must be horizontal because if one wing tilts into the water, as in the disastrous landing, the impact on the wing causes that point on the airplane to suddenly stop and the rest of the airplane to suddenly rotate around it. The wing will probably be ripped off the fuselage as the airplane cartwheels over the water and the other wing may be thrown off by the rotation. Either way, the passengers and crew will likely be killed in the crash and the ripped-open fuselage will rapidly sink.

As you know, Flight 1549 lost power in both engines because of impacts with birds, which were probably ground up within the engines. Using the flaps, Captain Sullenberger managed to sharply turn the airplane and put it into a glide down toward the Hudson River. He also used the flaps to slow the airplane because a high-speed impact with the water would have split open the fuselage. The trick, however, was to avoid slowing the airplane so much that it stalled. Stall does not mean that the airplane stops --- rather it means that the lift generated by the air passing the wings is no longer a match for the gravitational pull on the airplane. So, the airplane would have fallen instead of gliding.

I think the need of level wings and a slow speed are obvious. What is a bit more subtle is that the airplane needed to be nose-up by about 12º when it touched the water. It certainly should not be nose-down because the impact on the nose would have suddenly stopped the nose, and then the rest of the airplane would have flipped up and over that point and slammed upside down onto the water.

But why is a nose-up angle of about 12º desirable? What is more dangerous about an angle of, say, 25º? The main reason has to do with the direction of the impact force on the fuselage when the fuselage first hits the water.

Captain Sullenberger gradually lowered the airplane so that the upward impact force would be small, but the airplane was still moving forward at an appreciable speed. That meant that the force in the impact was mainly toward the rear of airplane rather than vertical. Sullenberger wanted that impact force to be directed along the length of the underside of the tail section. If the tail hit the water at a steep angle, rather than at a glancing angle, the impact force could have snapped off the tail.

Captain Sullenberger was flying an Airbus A320 like the one shown in this photo. Notice how the underside of the tail section slopes upward. If the airplane is nose-up by about 12º in a crash landing, that sloped tail surface is nearly horizontal, which means that the impact force from the water was directed along its length rather than at a steeper angle. Thus the tail did not break off.

The other reason for the nose-up angle has to do with what the rest of the fuselage does when the impact suddenly stops the tail section --- it rotates around the impact point and down to the water. If the rotation is only a few degrees, the fuselage does not pick up much rotation speed and thus tends to merely plop down on the water. However, if the angle is larger, the fuselage picks up more rotation speed and might slam down on the water. Obviously slamming the fuselage is never a good thing to do. As you can see in the Flight 1549 video link above, Captain Sullenberger held the nose of the airplane up by about 12º until the tail touched the water. And then the fuselage almost gently plopped down on the water.

After all, an airplane is very heavy. However, it has lots of air-filled compartments that water could not fill immediately. Instead the water had to seep into those compartments through fairly narrow openings. The airplane was like a leaky rowboat --- it certainly will sink but, as long as the fuselage is not cracked open, it will not sink immediately.

All in all, I don’t want to be on an airplane that must crash land on water but if I must be in that situation someday, I want Captain Sullenberger at the controls, holding the wings level, cutting the speed as much as possible without stalling, and holding the nose up by about 12º.

1.219 Charles Taylor’s one-wheel vehicleJearl Walkerwww.flyingcircusofphysics.comApril 2009 In the 1950s and 1960s, Charles F. Taylor designed and built a number of single-wheel vehicles, including the one shown here in the photo. Although the vehicle moved on a single wheel, it was balanced, even when stationary. Here are some links to videos showing Taylor riding on the vehicle:

However, the balancing for the scooter is provided by the rider and surely must take practice. The balancing for Taylor’s vehicle is provided by gyroscopes and the shifting of on weights on the vehicle.

A gyroscope is not easy to understand because its motion involves angular momentum and torque. A simple explanation is that once a gyroscope is set spinning about a certain axis (the rotation axis), it tends to remain spinning about that axis unless a torque from a force acts on it.

On Taylor’s vehicle, a gyroscope at the front spun around a vertical axis and one at the rear spun around a horizontal axis. Roughly speaking, the front gyroscope stabilized the vehicle against tilting to the front or rear, and the rear gyroscope stabilized it against tilting to the rider’s right or left. However, turning the vehicle required allowing a certain amount of tilt so that the gravitational force caused the gyroscopes to precess.

You’ve seen such precession with toy tops and gyroscopes. If you spin a top on a floor with it rotating around an axis tilted from the vertical, it does not simply fall over. The gravitational force certainly pulls downward on its center of mass, but the torque due to that downward causes the rotation axis to move in a circle around the vertical. That circling motion is precession. When Taylor wanted his vehicle to turn, he caused it to tilt so that the gyroscopes will turn the vehicle via precession.

1.220 Spaghetti breakingJearl Walkerwww.flyingcircusofphysics.comJune 2009 Richard Feynman is best known for his work in quantum field theory, nanotechnology, or several other esoteric subjects, but he is also known for introducing this culinary puzzle: If you bend a strand of dry spaghetti into a circular arc and gradually increase its curvature until it breaks, why does it break into three or more pieces instead of just two?

After all, once a break occurs at the weakest point along the circular arc and the stress and strain of the forced curvature is relieved, shouldn’t the remaining two pieces (one in each hand) simply oscillate for a short time and then come to rest so that you finally have two pieces? What would produce a third, fourth, or fifth piece? Feynman reportedly littered his kitchen with broken strands of dry spaghetti while seeking an answer.

Feynman’s puzzle was finally solved in 2005 in a paper by Basile Audoly and Sebastien Neukirch of Laboratoire de Modelisation en Mecanique, CNRS/Universite Paris VI in Paris, France. These researches produced a mathematical model of how a slender rod of brittle material can break when it is released from an initial curved state. Then they compared their model with tests using three sizes of Barilla brand spaghetti strands.

With both their model and actual spaghetti strands, they clamped one end of a strand in place and then bent the strand into a circular arc (the lower curve in Fig. 1). The curvature was significant but not quite enough to break the strand.

Then they released the unclamped end of the strand so that the strand began to straighten out (the upper curve in Fig. 1). In both the model and the high-speed photography with actual spaghetti, they found that the release produces a pulse of increased curvature that moves from the unclamped end toward the clamped end. Moreover, as this pulse travels along the strand, the increased curvature it forces in the strand can exceed the curvature the strand can withstand. At some point where the strand is a bit weak, the strand can break. Thus, once the unclamped end is released, the strand may not simply oscillate because the increased-curvature pulse may find a weak point and break the strand into two pieces.

Ok, now for breaking a strand by hand. Hold a strand with a hand on each end and gradually increase the strand’s curvature (Fig. 2). At some point the curvature exceeds the limit the strand can withstand at some weak point, and so the strand breaks there. In Figure 3, I arbitrarily show the break occurring near the midpoint.

Just after the break, each remaining piece of the strand is like the released strand in Fig. 1. That is, an increased-curvature pulse moves along each piece from the free end to the hand-held end. Each pulse can break the piece if the increased curvature exceeds the curvature limit at a weak point along the way. In Figure 4, I show two additional breaks, which leaves the strand in four pieces. However, each additional break releases another pulse, which could cause an additional break.

Auduoly and Neukirch calls this process cascading failure ─ the first break produces pulses that can then cause secondary breaks, which can then produce pulses that can then cause tertiary breaks, and so on. The process becomes less likely as the remaining hand-held pieces become shorter, and the possibility of breaks depends on the actual distribution of weak points, so we cannot predict the final number of pieces for any given strand. Still, we can now see why a dry strand of spaghetti probably will not break into only two pieces as common sense would predict.

1.221 Pub trick --- hanging a bottle on a wallJearl Walkerwww.flyingcircusofphysics.comJune 2009 How can you hang a bottle on a wall? Here are two photos of a bottle I hung on fiberboard that serves as a door to a small closet in my basement. And here is a video showing how to set up the trick. It is usually done with the bottle in a corner to gain more support, but if you are careful, a flat wall will do.

The trick will not work with many common walls but usually works with walls painted or stained with latex paint, which gives a good clue as to the physics of the trick. To hang a bottle on such a wall, you press reasonably hard on the bottle while you force it up and down along the wall through a short distance, trying to move along a line rather over a broader area. With a few strokes, you should feel an increase in the resistance to the motion and eventually be unable to move the bottle. You can then let go and the bottle will probably stay on the wall for hours or even days. However, placing a cushion or a catch box under it is a good idea. Also, be aware that the rubbing usually leaves marks on the wall, so don’t do this on a good wall (or on a pub wall, unless you just really want to “dance” with the bartender).

Anyone can do the trick but the real challenge is to explain it. Some of the videos on the web allude to friction or a roughening of the wall by the rubbing. Indeed, the increasing resistance you feel while rubbing the bottle is certainly due to a frictional force. Can that force prevent the gravitational force from pulling the bottle off the wall?

The gravitational force acts on every atom in the bottle but we can say that it collectively acts at the center of mass of the bottle, which is located at about the center of the bottle, as suggested in the first figure here. However, as suggested in the second figure, that force acts along a line of action that does not pass through the point where the bottom of the bottle touches the wall. That means that the gravitational force creates a torque around that bottom point, tending to rotate the bottle around the point and thus off the wall.

The upward frictional along the wall certainly counters the downward frictional force, but what counters the torque due to the gravitational force? The answer is that at the points where the bottle touches the wall, the bottle must adhere to the wall. When you rub the bottle along the wall, you slightly warm the latex paint, making it sticky. When the bottle stops and the paint cools, the glass and the wall are glued together. As the gravitational force tends to torque the bottle around the bottom contact point, the “glue” counters the torque.

You can see evidence of the gluing when you peel the bottle from the wall ─ part of the paint is left on the bottle at the contact points. Other wall surfaces (other paints) do not display this gluing effect because they do not become sticky when rubbed. Also, I cannot hang a can on a wall (or even in a corner). I think the reason is that, as I rub the can on the wall, the can conducts the thermal energy away from the contact points so rapidly that the paint does not warm sufficiently to become sticky. I could be wrong about this. Perhaps the sticky paint just does not stick well to metal. You might check this out and also investigate what other types of containers can hang from a wall, and what kind of wall surfaces work.

1.222 Pizza tossingJearl Walkerwww.flyingcircusofphysics.comJuly 2009 Tossing a pizza in order to stretch it to the size of the pizza pan requires not only a certain skill but also a bit of physics. Here is a video of what is called the single-toss technique, in which you see Tony Gemignani sling a rotating pizza into the air.

You can describe the stretching tendency in terms of a radially outward (centrifugal force) but physics instructors generally avoid that term because such a force is generally not a real force, only a convenient explanation.

If you take a fast turn in a car, you have the sensation of being thrown outward by a centrifugal force because your torso leans outward. However, your torso is merely trying to move in a straight line as a radially inward force (the friction on your rear end from the car seat) causes you to move into the turn. On the rotating pizza, the rim continuously tries to move in a straight line but, because it is attached to the rest of the dough, it is forced to move in a circle. Still, if the dough yields, the pizza grows larger with the rotating toss.

I have long been fascinated by pizza tossing but never understand the physics of the toss until I read a recent paper by K-C. Liu, J. Friend, and L. Yeo of Monash University in Melbourne, Australia. Here is their explanation:

Let’s start with the common single-toss technique, and let’s assume that you support the pizza with your left fist (knuckles upward) and drive the pizza into rotation with your right hand (palm upward). The pizza begins at rest with your right hand to your left side. As Gemignani tells us in the video, you support the pizza with your left fist as you bring your right hand rightward across your body. Now here comes the physics bit: your right hand is covered with slippery flour but you don’t want the hand to slip. Instead, you want to maintain contact with the pizza so that your right hand gives the pizza as much rotation as possible.

If the hand does not slip, we describe the frictional force between the hand and the pizza as a static frictional force. Such a frictional force always matches your force on the pizza --- if you increase your force, the friction increases to match it. But there is an upper limit to the static frictional force. If your force exceeds that limit, the pizza begins to slip and you will not be able to rotate the pizza very fast.

The value of the upper limit to the static friction depends on two factors: (1) the structure of your palm and the pizza dough (you cannot anything about this) and (2) the pressure between the pizza and your hand (you can do something about this). By pushing upward on the pizza while you rotate it from left to right, you increase the pressure and thus increase the upper limit to the friction. Now you can maximize the rotation you give the pizza before it leaves your hand. A pizza tosser already knows all this, perhaps through early training on the job. You can see the technique in Gemignani’s video --- as he rotates the pizza with his right hand, he brings his hand up so that the hand and the pizza move through a spiral.

With the single-toss technique, you catch and stop the pizza (both its flight and its rotation) and then repeat the process. Each toss widens the pizza until finally it is ready for the pan and the oven. A multiple-toss technique is different because when you catch the pizza, you don’t want to stop it. So, you might start with a single-toss technique but then when the pizza comes back down, you want your right hand already moving rightward so that contact does not slow the rotation. You also want your right hand moving approximately horizontally instead of up into the pizza. However, shortly after you make contact, you can begin moving your right hand upward. So, in the multiple-toss technique, your hand follows more of an elliptical path than a spiral, and you probably only use one hand, either palm or fist. You can see the motion in this video by Gemignani as he competes in a pizza tossing contest (yes, a pizza tossing contest).

http://www.youtube.com/watch?v=9uZeP7CX6lc&feature=relatedFor such tricks, Gemignani uses a tougher dough so that it does not easily stretch out during a toss. In fact, the pizza “disk” is tough enough that Gemignani can roll it for a short distance along a table or across the back of his shoulders.

Physics is everywhere, and if you want more pizza physics, come to The Flying Circus of Physics book where I describe why hot pizza can burn the top of your mouth whereas equally hot coffee will not (item 4.42) and why pizza with real cheese will develop lightly browned spots whereas pizza with fat-free cheese will not (item 4.47).

1.223 Pub trick ─ tying a ring hitch Jearl Walkerwww.flyingcircusofphysics.comJuly 2009 Allow a vertical loop of string to hang from your fingers and then slide a metal or plastic ring up the string from the bottom until it is near the top. Then let the ring fall. Not surprisingly, it simply falls down the string and onto the floor. However, if you use a bit of physics, the ring ends up tied to the bottom of the string in a ring hitch, instead of falling to the floor. No, there is no sleight of hand in which the ring snaps onto the string or you initially tie the ring to the string.

You can demonstrate the trick in a pub and then hand the loop and ring to someone with this challenge, “Now, let’s see if you can do it.” And, of course, they cannot.

As the video explains, you need to hold the ring with your fingers parallel to the plane of the string loop, with one finger slightly under the ring and your thumb on the opposite side of the ring. Then you need to release the ring by moving your thumb away from it, keeping your underlying finger in place. Doing so causes the ring to rotate around the underlying finger ---- the gravitational force effectively pulls on the ring’s center of mass, which is at the center. Because that point is displaced from the underlying finger, the force creates a torque around the underlying finger.

If the underlying finger is properly parallel to the plane of the string loop, the rotation causes the ring to wrap up the string as it falls.

My photos here depict stages in the wrapping process as though the underlying finger is on the far side of the ring, so that near side first rotates downward. In the third photo, note that the string is wrapped on the left and right of the near side of the ring. It the wraps stay on the near side instead of sliding to the rear side as the fall continues, the ring ends up in a ring hitch as it hits (and slightly bounces) at the bottom end of the string.

Although they immediately sense that rotation is required, most people cannot work out how the trick is done especially if you have practiced enough that you can perform it quickly.

1.224 Worm grunting and the sandworms of DuneJearl Walkerwww.flyingcircusofphysics.comNov 2009 Worm grunting is a quaint procedure for enticing earthworms to come to the surface, where they can be collected and then used as fishing bait. First, a wood stake is driven into the ground in reasonably moist earth (where worms tend to collect). Then a sturdy metal strip or rail is pressed down on the edge of the exposed end of the stake and rubbed across it. The strip does not move smoothly but undergoes stick and slip as it alternately catches and then releases on the wood. As a result, both strip and stake oscillate and emit a low-frequency sound (hence the name “grunting”).

The action is similar to fingers being drawn across a chalkboard, but the resulting sound is at a much lower frequency (less than 500 hertz, near the lower end of the human range of hearing) because the stake and strip are much longer than a fingernail. The oscillation of the stake sends sound waves through the ground, signaling worms to emerge from their burrows.

A similar technique is described in the classic science fiction series of books and movies with the general title of Dune. On the planet Arrakis, consisting largely of deserts, the inhabitants (the Fremen) coax giant sandworms out of the sand by attaching a thumper to the desert floor. The pounding by the thumper sends seismic waves through the thick layer of sand, and a worm with a length of several hundred meters (or even two or three kilometers) emerges. The Fremen climb up onto the worms to ride across the desert. My guess is that Frank Herbert, the author of the Dune books, got the idea from the practice of worm grunting.

Giant worms are also the star of the science fiction movies with the general title of Tremors. In this story line, man-eating worms are sensitive to the seismic waves sent through the ground by anything moving on the ground, even a person walking across it.

Although worm grunting sounds like folklore, recent scientific investigations demonstrate that (1) worms respond to the waves within minutes and (2) that the number of worms coming to the surface decreases with distance from the wood stake, corresponding to the decrease in the strength of the waves with distance. In fact, the ground oscillations can be felt by hand at a distance of several meters from the wood stake, and instruments could sense them at least 12 meters away.

The seismic waves traveling from the stake and through the ground are a form of a longitudinal wave (or sound wave, for short), which means that as a wave passes through a material (here, the ground), the material oscillates to-and-fro parallel to the wave’s direction of travel. (The other general type of wave is a transverse wave, where the material oscillates perpendicular to the wave’s direction of travel. A water wave is a common example.)

Some animals that prey on worms have figured that sending waves through the ground brings out a free lunch: Wood turtles stomp their front feet, and some birds either slap the ground with the feet or peck vigorously on a rock so that, as the wood stake, it sends waves through the ground.

Researchers do not know exactly why the oscillations provoke worms to emerge from their burrows, but two theories have been proposed: (1) Rainfall produces ground oscillations in about the same frequency range, and worm know to surface during rainfall to avoid drowning as the ground becomes soaked. So, sensing oscillations in that range, the worms might think that rain is about flood their burrow. (2) As they dig tunnels through the ground, moles produce seismic waves. So, the worms might emerge because they think they are fleeing from a hungry mole. (This second theory was advanced by Darwin.)

How did someone discover that the longitudinal waves generated by worm grunting brings out worms? Well, perhaps someone noticed the effect while digging a garden or plowing a field. Or perhaps, just perhaps, on a day of utter despair over his grade in a physical chemistry class, someone threw himself on the ground and repeatedly pounded it with his fists, and then noticed that he was surrounded by worms. (Worms don’t like PChem classes either.)

1.225 Pub trick---champagne cork as a mortar roundJearl Walkerwww.flyingcircusofphysics.comJan 2010 I am posting this as a pub trick, but it is actually a sure-fire way to get yourself kicked out of a pub and maybe even end up in court for assault. The trick is this: by aiming a champagne bottle as you open it, can you hit a target with the cork propelled from the bottle? Here is a video example:

When in the bottle, the cork is under a large pressure of 400 to 600 kilopascals (60 to 90 pounds per square inch) because of the carbon dioxide released by the fermentation process. That is about three times the pressure in a car tire. As the cork is worked free of the bottle, the high pressure shoots the cork out at a speed of about 13 m/s.

More simply, you can measure how high it goes when shot vertically upward. If we neglect the effect of air drag on the cork, the ejection speed (meters per second) is equal to the square root of the product of twice the acceleration of gravity (9.8 meters per second-squared) and the height (meters):

speed = square root (2gh).

The ejection speed tends to be larger for bottles with more gas volume (lower liquid level).

In the bottling process, a cork is squeezed into the neck of the bottle with a 65% reduction in its volume, to make a tight fit and to hold against the internal pressure. Newer corks are typically difficult to remove because of that fit, but older corks have been compressed so long that the cork cells have collapsed, loosening the fit. That means that the older corks are relatively easy to remove and, in fact, may shoot out unexpectedly, perhaps even because of slight shaking of the bottle. To be on the safe side, treat the bottle as a firearm and never point it at anyone or yourself until the cork has been removed.

http://www.mattonimages.co.uk/images/search/champagne+cork Many images of corks being shot out of a bottle. Note that there are several pages of images --- use the control at the upper right. And note that there is a “Find similar” option for each image. Some of the images are composites constructed on a computer. Can you tell which ones are composites?

1.226 Knight Rider stuntJearl Walkerwww.flyingcircusofphysics.comJan 2010 In the classic television show Knight Rider, Michael Knight (played by actor David Hasselhoff) drives a futuristic car called KITT and rights the wrongs done by bad guys. The car was modeled on a 1982 Pontiac Firebird Trans Am but had some very advanced features, including artificial intelligence. When the car required repair or concealment, it would be driven up into a moving semi-trailer truck, by means of a ramp that extended down to the road from the open rear doors.

We are all accustomed to faked stunts in movies, television, and web-based videos. So, in the last few years the validity of the car-into-the-truck stunt has been widely debated. Could it really be done? Or was it just sleight of hand (or rather, camera trickery)? If a car were actually driven up a ramp and into the open backend of a semi-trailer truck, wouldn’t it slam into the front of the interior?

Recently, the television show Mythbusters attempted to recreate the stunt without any camera trickery. The video that is now posted on the web is in two parts, the verbal discussion (it is linked at the bottom here) and the actual attempts (linked here), first at about 35 miles per hour and then at about 55 miles per hour. In the first attempt, be alert to the rotation rate of the tires as they come up onto the ramp, first the front tires and then the rear tires.

The hosts were concerned that the car would be propelled up into the truck and thus into a crash at the front of the interior, but afterwards they explain that the car’s large inertia (mass) was the saving factor. Here is the way I explain their success.

When a car accelerates from rest, the engine forces two of the four wheels to rotate. On a rear-wheel drive car, as the 1982 Firebird Trans Am, the rear tires are forced to rotate. Let’s take the view that the car accelerates to the right. Then in our view the rear tire is being forced to rotate clockwise, which tends to slide it leftward on the road.

Provided that there is good “grip” between the tire and road, that rearward motion is prevented by a forward frictional force on the tire from the road. It is that force that propels the car along the road. (If the road were very slippery, as on wet ice, it would not be propelled.)

As the car moves, the front wheels also begin to rotate clockwise but not because of the engine. Instead, the motion of the car tends to slide the front tires toward the right, which means that the road exerts a frictional force to the left on them. That (small) force causes the tires to rotate clockwise.

Now let’s switch to the stunt. As the front wheels come up on the ramp, they are suddenly on a surface that is moving at about the same speed as the car. They are still rotating clockwise, which means that they tend to slide rearward on the ramp. Provided that there is enough grip between the tire and ramp, a forward-directed frictional force from the ramp prevents this slippage.

As you see in the first attempt in the Mythbusters recreation, the rotation of the front tires is almost immediately eliminated by the forward-directed frictional force. The show’s hosts were concerned that this force might propel the car up into the truck so severely that even if the driver applied the brakes, the car would crash. However, the force was small (not much is needed to stop a front tire from rotating) and it was also very brief. Thus it had no chance to propel the car forward.

Something similar happened when the rear wheels came up on the ramp. They too were turning rapidly clockwise and tended to slip on the ramp, but the frictional force that countered the slippage almost immediately stopped their rotation. This force was also too brief and weak to propel the car forward. Of course, as soon as the rear wheels came up on the ramp, the driver had to ease his foot off the gas pedal, or the engine’s forced rotation of the rear wheels could have greatly increased the frictional force on the rear tires, which would have accelerated the car up the ramp and probably into a crash.

The same stunt is shown in the first version of the movie The Italian Job (the one with Michael Caine). The clip is no longer available on the web, so you'll have to rent the movie. In it we see three small cars racing down the road with stolen bars of gold. When they come up on a bus, we discover that the interior of the bus is empty and that the rear doors swing open so that ramps can be extended down to the road. Then one by one, the cars are driven up the ramps and into the bus, to hide.

I am sure that some camera tricks were used to film the scenes, but we do see a very credible shot of one car making three attempts to get up the ramp. If you get the movie, watch the front wheel on the second and third attempts --- the wheel stops on the ramp. Here again we see that the forward-directed frictional force on the tire from the ramp is enough to prevent the tire from slipping. We also see that the force is insufficient to propel the car into the bus. Indeed, the tire rests on the ramp and the driver apparently had to apply the gas pedal briefly to get the rear wheels up on the ramp and the car into the bus.

A truck is normally fairly stable because of the separation of its left-side wheels from its right-side wheels. Any chance lifting of the truck by a wind gust is quickly righted. The problem, of course, is that the side of the truck presents a large surface against which the wind could push. In a physics class, we say that the force from the wind creates a torque around the rotation axis. In the video that axis runs under the wheels on the left side.

What we see in the video is the result of a very strong wind. The truck could have stabilized had its center of mass not reach the point above the rotation axis. However, once that critical point is reached, the truck is unstable and even a slight wind or a slight bump in the road could finish the rotation. The truck was then much like a domino being toppled over.

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1.227 Standing and walking in a strong windJearl Walkerwww.flyingcircusofphysics.comDecember 2014

When you stand, your center of mass is above your support area, the region on the ground that connects your feet. You already know that if you lean forward without moving your feet, you will fall over. That fall is due, of course, to the gravitational pull on your body. We can assume that the pull is a force vector acting at your center of mass. When the center of mass is not over the support region, the gravitational force produces a torque around the support region and you will rotate around that region and onto the ground, face first.

Now suppose that you are facing into a strong wind. The force of the wind produces a backward torque that tends to rotate you in the opposite direction and onto the ground, rear end first. To counter that wind torque, you lean forward such that the gravitational torque and wind torque approximately balance.

Walking is even trickier. Normally, you step forward such that the gravitational torque begins to rotate you but then you stop the fall with your forward foot. However, in a strong, gusty wind finding the right lean and the right timing of the forward step can be difficult. As you can see in these following videos, some people attempt to walk in a steady effort, others crouch so as to minimize their cross-sectional area in the wind (to reduce the wind’s total force), and others hop forward. .

1.228 Lucky shotsJearl Walkerwww.flyingcircusofphysics.comFeb 2010 Did you ever see a game-winning, last-second shot in a sporting event, where the odds of making the shot were almost zero and yet the athlete somehow made it? Here are videos of several examples in basketball:

From any given position on the basketball court, there are a range of launch speeds and a range of launch angles (up and down and also left and right) that will put the ball through the basket, “catching only net” (not bouncing from the rim or basket support). However, for a long distance shot, the speeds are large and the range is narrow, and throwing the ball as hard as you can usually means that you lose control of the ball and thus miss the required angle.

In an actual game, of course, you have only one try before the play resumes or the game ends. However, if you are by yourself with a video camera recording your shots, you can repeat a shot hundreds of times until you happen to make a basket. Then you need only to edit out the bad throws. You can also practice shots that would not be practical in a real game, such as bouncing the ball from the floor, ceiling, or wall and into the basket.

If the ball hits, say, a floor with little or no spin, the angle of its bounce is about equal to the angle of its approach, as shown in the first figure here. During the collision, the ball partially collapses in the contact area and experiences a force from the floor that is approximately perpendicular to the floor. That force propels the ball away from the floor. The ball is still moving to the left but now it is also moving away from the floor. The combined motion takes it along a path that is angled relative to the vertical about the same as its initial path.

Putting spin on the ball can noticeably alter the angle at which it leaves the floor because of the friction the ball encounters in the collision. As indicated in the second figure here, if the ball is spinning clockwise when it hits the floor, it tends to slide leftward on the floor. That attempted motion produces a frictional force to the right on the ball. So, during the collision, the ball experiences two forces from the floor: the perpendicular force and also the rightward frictional force. The latter rotates the rebound path toward the vertical, and the ball can take a surprising bounce from the floor.

If the ball initially has a counterclockwise spin, the frictional force is to the left and the bounce is then at a larger angle to the vertical.

Hitting the basket with a normal throw is hard enough, but trying to control the spin rate to get the proper bounce angle is very difficult. Still, with enough practice and a continuously running video camera, it can be done and recorded.

There is a limit to how far you can throw a basketball. The limit is partially set by your muscle strength but it also set by the distance along which you propel the ball. In the propulsion, we do work, which is defined to be the product of force and distance. Athletes build up their muscles to be able to provide a larger force but they also maximize the distance. With the normal basketball shot, as in a free throw, the ball is propelled from near the head to full-arm extension. In the underhanded free throw that is no longer popular, the ball is propelled along a longer path, from about waist level out to almost full-arm extension. The legendary player Rick Barry used the underhanded throw when he set the record for free throws, but he never used it in field shots because the long path length would have given an opponent plenty of opportunity to block the shot.

Here is a novel way of greatly increasing the path along which a player does work in launching a ball.

I don’t think the young man had enough strength to give the ball enough energy to travel the length of the court with a normal throw. But with the longer path length provided by the somersault, he easily threw the ball that far. The same novel way of throwing recently put Danny Brooks in the Guinness book of records for longest throw-in of a (soccer) football, almost 50 m.

Parts of the video (such as throwing two American footballs) seem ok but the rest seems fake (even the sound effects seem to be dubbed in).

In a video, discerning an amazing toss from a fake one can be difficult. Are the tosses in this next video real? (You might turn off the audio, which is just music and which contains a rude word, unless, of course, you like rude words.)

1.229 A truck falls over onto on a carJearl Walkerwww.flyingcircusofphysics.comMarch 2010 This video shows a horrible scene --- rescuers frantically attempt to lift a truck off a car that it has fallen onto and crushed almost to street level. Amazingly, they find the driver unharmed.

We can easily argue that the driver survived because he leaned over onto the seat as the truck began to compress and collapse the roof of his car. Then the truck’s descent was stopped by the engine block, allowing the man a tiny amount of space. We can also easily argue that the wall of the truck might have yielded and thus not fully pressed against the car.

I think there is one more argument, one that is based on an earlier story here. If you crumple up a sheet of paper as tightly as you can, about 75% of the ball is still filled with air. It is not the air that prevents you from making the ball any tighter. Rather, it is the required energy.

As you begin to crumple up the paper, you begin to create ridges and d-cones (the junctions of ridges), as you can see in this photograph. Each time you tighten the ball, you break existing ridges into more ridges that are shorter and more tightly folded, and that requires energy from you. You quickly reach the point where you cannot provide enough energy to make the next set of ridges.

So it goes with the crumpled metal of the car in the video. As the truck began to compress the car, it began to produce ridges and d-cones. The energy for them came from the gravitational potential energy of the truck. Normally when an object falls over, the gravitational potential energy is converted into kinetic energy of the object ---- it moves faster. But here the potential energy is put into the ridges in the crumpled metal. The truck quickly reached the point where any further descent did not provide enough energy to produce more ridges, and that is where the truck came to rest.

Of course, cars are commonly crushed in junk yards so that the metal can be reused. Such a junk-yard car is placed between two very thick, strong plates in a hydraulic press. As one plate is forced toward the other plate, the car metal yields and folds into ridges and d-cones. Although the press might develop a huge pressure of 2000 pounds per square inch (13 million newtons per square meter), crushing the car is more complete if the pressure is applied sequentially to sections of the car. In this video, watch how the front of the car is pressed down first and then the rear of the car is pressed down. Notice also how the forklift is used to dent and rip the vertical panels of metal to weaken them.

A section of metal can be very strong against compression along its length but once it is dented, the section becomes very weak. You can demonstrate this transition with an empty pop or beer can. If you carefully step up on the can with one foot, it can support your weight because the downward force on it is along the vertical sides. The can will almost immediately collapse if you shift your weight so that your force on the can is at angle to the vertical or if someone strikes the side of the can with a rod, denting the wall.

1.230 Pub trick --- removing a coin from under a mugJearl Walkerwww.flyingcircusofphysics.com

March 2010 On a firm table with a standard tablecloth, two stacks of coins are arranged so that they will be able to support opposite sides of a mug of beer. A last, thin coin is placed between the two stacks, and then the mug is put into place, straddling the two stacks. The challenge is to remove that last coin from beneath the mug without touching it or the mug. Here is the video solution (though the written instructions in it seem to be inconsistent):

As with any pub trick, once the solution is known, anyone can do the trick. The real challenge is to explain the trick: How does it work?

The physics at work here is similar to a common stunt in which a tablecloth is pulled out from beneath a set of dishes on a table. If you pull slowly, the frictional force on the dishes from the tablecloth is strong enough to force the dishes to move with the tablecloth. Of course, if you continue to pull, the dishes come off the table and onto the floor. The frictional force in this situation is said to be a static frictional force because the plates and the dishes do not slide relative to each other.

To avoid breaking the dishes, the trick is to yank the tablecloth so that it immediately begins to slide under them. That relative motion means that the frictional force is a kinetic frictional force, which is less than the static frictional force and may not be enough to move the plates at all.

In the pub trick, you hold the far side of the tablecloth firmly against the table while you scratch the tablecloth on the near side, next to the mug. Each time your nail catches the threads of the tablecloth, they are stretched toward you and so are the ones farther from your finger and under the mug. The ones under the coin move the coin slightly toward you. The coin is like the dishes that move with the tablecloth when it is gradually pulled.

Each time your nail releases the threads, they act like springs and attempt to snap back to their initial positions. This retreat is so sudden that the threads slide under the coin without moving it. The coin is then like the dishes that do not move when the tablecloth is yanked. Thus, with continued scratching, you gradually shift the coin toward you until it moves out from under the mug.

April 2010 Roller derby is an action-packed game played between two teams on roller skaters that race around an oval track. Points are made when one team’s “jammer” manages to pass by any of the “blockers’ on the other team. The blockers do their best to block the opponent jammer or knock her off balance or even out of the oval. The interactions are rough but mostly theatrical.

When I watched roller derby on television as a teenager, I was fascinated by the whip move in which a blocker can propel her jammer past the opponent jammer or a blocker. As they roll forward, the blocker reaches back to grab the hand of her jammer, and then together they pull on each other so that the jammer is flung forward. Here is a video that shows the early style of roller derby, the antics of shoving and punching, and the simplest form of the whip move.

The following video show a more refined version of the whip move, in which the blocker (Bonnie D. Stroir --- say it fast for the pun) begins to skate backward before reaching back to grab the hand of her jammer (Lemmon Drop). They then pull toward each other as the jammer is propelled forward.

In this next video, the blocker remains rolling forward while extending a leg to the rear, which is then grab by the striker. The leg is then brought sharply toward the team player’s chest in order to propel the striker forward.

Let’s consider the reverse-rolling version of the whip move (while actually skating instead being stationary just for the explanation). When the blocker and jammer lock hands, they become a system that is moving forward along the track. We can make a reasonable assumption that the retarding force from the rolling contact of the wheels on the track is negligible because the wheels are designed to rotate about their axes with negligible friction. Thus, within our approximation, there is no horizontal force acting on the system.

In such a situation, the members of the system can pull on each other, changing the individual speeds, but there is a property of the system that those internal forces cannot change: the momentum of the system.

Momentum is a common word with lots of meanings but it has a single technical meaning: It is the product of the mass and the velocity. The blocker and jammer each have momentum, and the sum is the momentum of the system. As the skaters pull on each other, the values of the individual momenta change but the total cannot change --- it is said to be conserved.

Let’s examine the momentum for the video example where the skaters are actually moving along the track. They have about the same mass and speed and thus about the same momentum. So, when they first lock hands, the total momentum is twice the individual values. After they pull on each other and then release hands, the blocker is almost stationary, with zero momentum. Because of the conservation of momentum, the jammer has all the momentum, twice as much as she had initially. That means that she has twice her original speed, plenty enough to race past the next opponents in her path.

There is another property of the blocker and jammer and thus of the system --- kinetic energy, which is the energy associated with the motion. That energy is defined to be half of the product of mass and the square of the speed. As with momentum, the system’s kinetic energy is the total of the individual amounts. However, the system’s kinetic energy is not conserved in the whip move because the players obviously work hard to pull themselves toward each other. That muscular effort puts energy into the motion of the released jammer. Indeed, without the work done by the skaters in pulling themselves together, the jammer would be released with just her original speed.

Both momentum and kinetic energy are associated with motion, which we can see, but both concepts are abstract, not “warm and fuzzy” in an intuitive way. Indeed, scientists and engineers struggled for a great many years before they hit upon these ideas. Plenty other ideas were championed and then abandoned along the way, simply because they were not successful in providing insight into actual measurements. However, I doubt that any of the scientists and engineers in that effort would have foreseen the use of momentum and kinetic energy in the high-energy antics of roller derby.

Physics is everywhere, even (especially) in roller derby.

Oh, if you would like to see my calculations about the whip move (using only high-school level algebra and physics), watch the “Roller derby whip move” video at the Flying Circus of Physics page on FaceBook:

May 2010 Here is the challenge: You must move a small ball from one beer mat to another one using only a common wine glass, without touching the ball with anything but the glass. As shown in the following video, most people attempt to scoop up the ball with the edge of the glass, but that simply knocks the ball off its mat. The video also shows the proper way to meet the challenge.

As shown, you invert the glass and place it down on the mat with the ball inside. Then as you begin to move the glass around in a large circle, the ball climbs the interior and rolls around the widest point of the glass. If you continue to move the glass in a large circle, the ball is trapped even when the glass is picked up and moved over to the second mat. As you slow and stop the glass’s circular motion, the ball falls down onto the second mat and soon comes to rest.

As with any of the pub tricks here at the FCP site, my point is that anyone can do the trick but the real challenge is to explain it.

When you first begin to move the glass in a large circle, the rim bumps against the ball, scooping it up slightly into the interior. If you happened to stop the glass just then, the ball would simply fall back onto the mat. But by continuing to move the glass, the rim continues to press against the ball. That force on the ball is said to be a normal force, which means that it is perpendicular to surface at the point where the ball makes contact with the glass wall.

Because the wall is outwardly curved, part of that normal force is upward and provides support for the ball, preventing it from falling back down. The figure here shows the normal force on the ball and also the horizontal and vertical components of that force.

The vertical component supports the ball against the gravitational force, and the horizontal component is the centripetal force that is needed to make the ball move in a circle inside the glass.

The faster you make the ball move, the higher it goes on the glass wall until it is just below the widest section. It cannot move any higher because then the normal force would be horizontal and thus there would be no vertical component to support the ball.

A similar rising for a rotating object can be seen, of all places, in a common professional wrestling move. (For those you unfamiliar with this sport, let me say that it is highly theatrical but great fun to watch. It is not Olympic style wrestling.) Here is a video clip showing an extended use of the “giant swing” move, which is intended to make the opponent dizzy. Actually it probably makes both wrestlers dizzy, not only because of the rotation but also of the need for cooperation to prevent any injury.

Now you can not only explain the pub trick but tie it into any wrestling enthusiast who is hanging out in the pub.x

1.233 Snake slitheringJearl Walkerwww.flyingcircusofphysics.comAug 2010 Recent work published by David L. Hu (Georgia Institute of Technology and New York University), Jasmine Nirody, Terri Scott, and Michael J. Shelley (each of New York University) explains how a snake is able to slither by adjusting the frictional forces from the ground that act along its body.

The frictional forces depend on the coefficient of friction between the body and the ground and also on the downward force due to the weight of the body. The snake is able to increase the downward force in some parts by slightly arching its body in other parts. Thus it loads some parts by unloading other parts. The snake can then push horizontally on the loaded sections without them merely sliding over the ground, thus propelling itself.

The second key in the snake’s control over the friction is that the overlapping scales on its body have different coefficients of friction when pushed in different directions. The least coefficient is for forward motion, allowing for the snake to easily slide the unloaded sections forward. Compared to the forward-motion coefficient, the coefficient for motion toward the rear is about 50% greater and the coefficient for motion toward the side is 100% greater. Thus, the snake can push fairly hard toward the rear and toward the side without sliding in those directions.

Here is my sketch of the frictional forces at several spots on a snake based on a figure in the paper by Hu, Nirody, Scott, and Shelley.

The loaded sections are the points of inflection (where the curvature changes between concave up and concave down). The snake pushes in opposite directions on the two sides of a point of inflection, tending to rotate the body around that point. During the rotation, the snake also moves forward because the net force of all the frictional forces is in that direction. When you propel yourself forward, your feet push on the ground directly toward the rear. The snake must push toward the rear and also sideways in order to move forward, and it also must continuously adjust (1) which parts of its body are loaded and (2) in what direction it pushes those loaded parts. It also seems impossibly complicated, but the snakes do all this without taking a single physics or engineering class.

1.234 Pub trick --- picking up a glass with a strawJearl Walkerwww.flyingcircusofphysics.comOctober 2010 The pub challenge this month is to pick up a common drinking glass, say, a pint glass (because this is a pub challenge) with a common drinking straw without you directly touching the glass. Of course, there is no way you can slip the straw under the glass without overturning it. And even you can overturn it without breaking it, you cannot insert the straw into the glass and lift up, because the straw will merely buckle under the weight of the glass.

Here are video that show how to meet this pub challenge for three styles of drinking glasses.

As shown in the videos, first you bend the straw so that the horizontal part is slightly longer than the diameter of the glass. Then you place that part between the opposite sides of the glass while pulling upward on the vertical part of the straw so that the horizontal part becomes wedged. This works best if the glass has a rim so that one end of the straw catches on the rim. The friction between the wall and straw is then quite large even though the wall is smooth.

You can now lift the glass by pulling upward on the vertical portion of the straw. Because the force acting on the horizontal portion is at one end, that portion is much less likely to buckle than if it were acting at the middle. The fact that the straw is round instead of flat also decreases the chance of buckling.

After you practice lifting an empty glass, see how much liquid you can lift. The pub challenge might then be, “If you can lift it without spilling it, you can drink it.”

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1.235 Jumping out of a beachJearl Walkerwww.flyingcircusofphysics.comMarch 2011 Here is video that shows an athlete who is so powerful and quick that he can be buried in sand up to his neck and yet still be able to leap up and out of the hole and onto the beach.

Is this possible? Never mind whether the video is faked or not, is the leap even possible if the person is especially strong?

Let’s assume that the person has been buried in the sand in a crouching position, to be ready to leap out of the sand. If the sand surrounds the person, the grains will be locked into position, with so much friction between themselves and with the person’s clothing and skin, then to slide the person through the sand would require an enormous force. Indeed, the force would be so large that the person would injured.

Being trapped in sand is the nightmare of quicksand, which a pool of sand into which water flows. As I explain in The Flying Circus of Physics book, quicksand is a sand bed with a water influx, such as from a natural spring. The influx moves the grains apart somewhat and lubricates them so that they can slide over one another. If you step onto this arrangement, you can sink into the lubricated sand. If you struggle by trying to move your leg upward quickly, the quicksand suddenly becomes rigid and you cannot move the leg at all. The trouble is that sudden motion tends to increase the spacing between grains, but the sliding of grains against grains produces a lot of friction, preventing movement. So, if being trapped in somewhat lubricated sand means that you cannot move, how about being trapped in dry sand?

So, no one, not even a powerful athlete can jump out of a beach as we seem to see in the video? Of course with modern techniques, the whole video could be faked. But the video could have been partially real if the athlete was crouching in an empty pit with a sand covered cloth hiding the pit and surrounding his neck. Then there would be no sand along his sides and he could easily leap from the pit onto the beach.

If you would like to see a video in which I explain how packed grains can prevent motion, go to the Facebook site for The Flying Circus of Physics

and click on the video option on the left. Search for the video in which I explain how rice grains can prevent motion to Jay Ingram, the host of The Daily Planet Show on Discovery Channel Canada. (Right now it is the third video.) You can also find the video where I explain quicksand on the PBS show Newton’s Apple. (Right now it is the fourth video.)x

1.236 Bullet spinning on iceJearl Walkerwww.flyingcircusofphysics.comApril 2011 First a serious warning. This stunt is extremely dangerous. A person fires a handgun several times into layer of ice (on the ground or on a frozen lake). Sometimes, the bullet ends up rapidly spinning nose down. The videos here are real but firing a gun at nearby ice, especially with no eye protection, is just way beyond foolish.

As the bullet travels along the barrel of the gun, it is forced to spin by the gas propelling it and the rifling (spiraling) cut in the interior surface of the barrel. As the bullet flies through the air, the spinning stabilizes its orientation so that it remains in the streamlined position, with minimal air drag. That way, the gun can be aimed at a target with a good chance that the bullet will reach the target. Without spinning, the bullet would quickly begin to tumble, causing it to encounter significant air drag, and so it would just fall down.

If a bullet ricochets from ice, it might still be spinning rapidly. If it lands on the ice on its side, it will probably dig a slight impression in the ice and then spin until it loses all its rotational energy as it rubs against the ice. This may take a surprisingly long time because the bullet probably frequently bounces and thus does not continuously rub against the ice.

The surprising feature is if the bullet ricochets to a nose-down orientation. Then it can spin like a top or gyroscope. Such motion is magical because it involves physics that is not intuitive. A spinning top has a property known as angular momentum, which involves the spinning rate, the mass, and how that mass is distributed. A top can spin while standing straight up (it is a “sleeping top”). It is leaning over from the vertical, however, it will spin around its central axis (down through body, along the line of symmetry) as that axis moves around the vertical. That motion is called nutation and is notoriously difficult to explain without (or even with) math.

Here is a fast explanation. The gravitational force pulls downward on the top’s center of mass, causing a torque around the top’s pointed end on the ground. That torque gives the top a horizontal angular momentum. If the top is not spinning, that torque and the resulting angular momentum would just result in the top toppling over. However, if the top is spinning, it already has angular momentum. The new horizontal angular momentum adds to the existing angular momentum, resulting in a horizontal circling of the top around the vertical. So it goes with the spinning bullet also.

x1.237 Clown car physicsJearl Walkerwww.flyingcircusofphysics.comMay 2011 A delightful blog by John Pearley Huffman has recently appeared concerning the physics of a clown car. Just in case you have never seen this classic circus performance, let me describe it and give you a video link. A very small car is driven into the circus arena. Then, one by one, an impossible number of clowns emerge from the car. The act is surreal because there seemingly is far too little room in the car to hold all those clowns. If you are someone who finds clowns frightening instead of funny, this invasion of clowns from a small car is nightmarish.

In his humorous blog, Huffman wanted to calculate the number of clowns that can fit into a given clown car. If you assume a certain volume for a clown, then you might think that the number of clowns is equal to the volume of the car divided by the volume of a clown. However, the clowns are not a fluid and thus do not fill up the volume completely. There are bound to be empty spaces (voids) between the bodies no matter how tightly packed those bodies are. Besides, in order for clowns to be clowns, they need props in the car also. So, the calculation has lots of variables. Here is the link to Huffman’s blog:

Ever since we have had closed cars, there have been contests as to how many people can be packed into a car. For example, Huffman quotes one source as saying that 17 people were once stuffed into one of the original Volkswagen Beetles. The waitresses in this next video come close.

Dense packing of hard solid bodies in a container has long been a subject of interest to scientists and mathematicians. Usually, the studies are conducted with either spheres or oblate spheroids, not clowns, and results are quoted as a packing fraction. For example, if you fill a container with a fluid, the packing fraction is 1, meaning that the full volume is occupied by the fluid. For spheres, such as gum balls, the packing fraction is about 0.74 at best, meaning that 74% of the volume is occupied by the spheres and 26% is taken up by the voids. More fun, for M&M candies (which are oblate spheroids, with one diameter longer than the other) the packing fraction is 0.665.

A common contest involves guessing the number of M&M candies filling a fairly large, closed container with transparent sides, say, a one liter water bottle. Actually, with a bit of preparation, you can always get close to the correct answer, as explained in the following videos. The procedure is to measure the volume of the container and then the volume of an M&M candy. (To be more accurate, you measure the volumes of many individual candies and then average the results.) Then multiply the container volume by the packing fraction of 0.645 and divide by the individual candy volume. Simple. Harder would the question, how many M&M candies can you fit into a clown car?

1.238 Stacking of rods to produce a large overhangJearl Walkerwww.flyingcircusofphysics.comJun 2011 Here is a breathtaking example of stacking rods so as to construct a large network that ends up being balanced on a single point.Mädir Eugster of Rigolo, the Swiss Nouveau Cirque, begins with a short rod, with a center of mass located at its center. He balances that first rod by supporting it with a second rod. Then he balances those first two rods by supporting then with a third rod. Rod by rod, with brilliant control, he works his way through progressively larger rods until he has a network of rods stretching away from him, all balanced on a single point at his fingers on the last rod. Here is the video link. Try not to breathe as you watch:

There are some subtle points about the physics of this performance, but let’s start with the textbook stuff about a uniform rod (the mass is uniformly distributed along the rod’s length).

Every atom in the rod is being pulled downward by the gravitational force. However, rather than consider all those forces individually, we can lump them together and say that effectively there is a single downward force acting at the center of mass. Because the mass of the rod is uniformly spread along the rod’s length, that special point is at the midpoint of the rod. Eugster balances the rod by supporting it just underneath the center of mass.

If we switch back to thinking about the forces on the individual atoms, we can see that there is just as much downward force on one side of the support point as on the other side. So, like a seesaw or teeter-totter with equal weights on the two sides, the rod is in balance. If, instead, the support point is shifted away from the center of mass, the net force on one side would be larger than the net force on the other side and the rod would be rotated around the support point. That is, the rod would be torqued around the support point. To avoid this rotation, the Eugster wants as much weight on one side of the support point as on the other side.

When the first rod is balanced on the second rod, Eugster holds that second rod at the center of mass of the system of two rods. On one side of the support point (call it the farther side from Eugster), there is the weight of the first rod and part of the second rod. On the other side (the closer side), there is the weight of the rest of the second rod. The farther weight matches the closer weight. Each time Eugster inserts another rod, he wants a similar matching of weights. On the farther side, there is the weight of all the previous rods and part of the new rod. On the closer side, there is the weight of the rest of the new rod.

If the rods were all identical in length and uniform in the distribution of weight along their lengths, the balancing act would quickly become difficult or even impossible. Each new support point on a new rod would shift progressively closer to the previous rod, and the rods would begin to overlap. To avoid such an unwieldy situation, Eugster uses progressively longer rods with noticeable heavy ends on the closer side. (I assume these rods are actually tree branches but I don’t recognize the type.) Using this scheme, Eugster moves each new support point away from the previous rod and avoids overlapping the rods. Still, you might notice in the video that chance rotation brings some of the rods close enough to touching that he must adjust them. With each new rod, he holds the rod at the new center of mass of the full network of rods. Holding the new rod anywhere else would require him to fight the attempt by the gravitational force to rotate the network around his fingers. I think he has the positions marked on the rods so that he immediately knows where to hold the new rod and where the rest of the network should rest on it.

Although lots of papers have been published on the stacking scheme of blocks (especially off the edge of a table, so as to maximize the overhang), I don’t think anyone has analyzed this two-dimensional (well, really, three-dimensional) stacking scheme of rods. You might try at it.